CHAPTER 1

STATES OF MATTER

1.1 Introduction

Matter exists in three different physical forms. They are namely – gases, liquids and solids.

The molecules of the solids are held very close to each other. And the solids became of their close proximity between the molecules generally exits as compact masses. In the liquids, the arrangement of the molecules is not so compact when compared to solids. Hence the liquids take the shape of a container. In gases the molecules are very spaciously placed. They are very far from each other. The inter conversion of these three physical forms – solid-liquid-gases is possible (in a specified way and vice versa generally). But when we consider the solids with high vapour pressure, they directly convert into the gaseous state without passing through the liquid state. This process is called as sublimation, and the reconversion is known as deposition.

Sometimes the matter can also exist in another phase (4th phase) mesophase. It is also called liquid crystalline state which is an intermediate state between the liquids and crystalline solids.

1

2 | Physical Pharmaceutics – I

1.2 Binding Forces Among the Molecules Generally for the matter to exist in the form of liquid or solid or gas an association must exist between the molecules. The binding forces between the molecules are of different types.

Repulsive forces: When the molecules are brought so close that the outer charge causes them to repel each other like rigid elastic bodies.

The repulsion is due to the interpenetration of the electronic clouds of molecules and increases exponentially with a decrease in distance between the molecules. At certain equilibrium distance about (3 to 4) × 10–8 cm (3-4Ao) the repulsive and attractive forces are equal.

Attractive forces: Generally when two atoms or molecules are brought closer together, the opposite charges and binding forces in the two molecules are closer together than the similar charges and forces causing the molecules to attract one another.

(a) The attractive (b) Partially repulsive (c) Repulsive

denotes attraction denotes repulsion Fig. 1.1

Vander Waals forces: Generally the dipolar molecules tend to align themselves to form a group which became an attraction between the two opposite poles of the molecules. The South Pole is attracted towards the North Pole and vice-versa. These dipole-dipole interactions are called as keesom forces.

The dipoles are able to polarise a non polar molecule and there after aligns with them and that type of interactions are called dipole-induced dipole or debye interactions.

The nonpolar molecules are able to induce the polarity to each other there by resulting in induced-dipole-induced dipole interactions also called as London attractions.

The Vander Waals forces are applicable in the process of condensation of gases.

Solubility of drugs

Formation of some metal complexes and molecular addition compounds

Some biological processes and drug actions

States of Matter | 3 Generally the intermolecular forces like London forces, Keesom forces and Debye interactions are referred as Vander Waal’s forces. But generally the London forces alone are referred as Vander Waal’s forces because they are the interactions between the non-polar molecules.

Ion Dipole and Ion-induced Dipole Forces: These types of forces between the molecules are specially concerned with the parameter of solubility. And these interactions increase the solubility of substances.

Hydrogen Bonding: The bonding that exists between a molecule containing the hydrogen atom and strong electro-negative atoms is referred to as hydrogen bonding.

Hydrogen bonding is of two types.

Intermolecular Hydrogen Bonding: The hydrogen bond which is formed between two molecules is referred to as intermolecular hydrogen bonding.

e.g., Hydrogen fluoride Formic acid dimmer (CHOOH)

F-H---F-H

HOO

CH

OH O

CH

→ Hydrogen bond

Intramolecular Hydrogen Bonding: The hydrogen bond which is formed between two atoms of the same molecule is referred to as intramolecular hydrogen bonding.

e.g., Salicylic acid

OH

O

C

OH

Bond Type Bond energy (kcal/mole

(appron))

Vander Waals force and other inter molecules attraction

1-10

Dipole-Dipole interactions, orientation effect or keesom force

Dipole-induced dipole interactions, induction effect, Debye force

Induced dipole-induced dipole interaction, dispersion effect or

London force

4 | Physical Pharmaceutics – I Ion dipole interactions

Hydrogen bonds O-H---O → 6 C-H---O → 2-3

O-H---N → 4-7 N-H---O→2-3 F-H---F→7

The Gaseous State: Gases have neither definite shape nor definite volume as the molecules in this state are far apart from one another. They occupy the entire volume of any given container and their volume is assumed to be the same as that of the container. As the gas molecules travel in random paths, frequently colliding with one another and with the walls of the container in which they are confined, they exert a pressure.

The Ideal Gas Law: A gas which obeys all the gas laws under all the conditions of

temperature and pressure is called ideal gas. The gases which do not obey gas laws under

required conditions are called real gases. Real gases show the behaviour of ideal gas at

high temperatures and low pressures.

The ideal gas equation is obtained by combining the three gas laws. They are Boyles

law, Charles law and Avagadro’s law.

Boyles Law: It is defined as the volume of a given mass of a gas is inversely proportional

to pressure at constant temperature

P

1 V (or) P

V

1

PV = k (constant) …..(1.1)

Charles-Gay Lussac Law: At constant pressure, the volume of a given mass of a gas at

0 oC increases or decreases by 1/273 times its volume for every degree rise or fall in

temperature i.e., the volume of a gas increased linearly with increase of temperature if

pressure is constant

V T

V = kT …..(1.2)

Both eq. (1.1) and (1.2) are combined to obtain the relationship

T

PV = k (constant) …..(1.3)

The constant k depends upon the amount of the gas. We can understand from

Avagadro’s law.

States of Matter | 5 Avagadro’s Law: It states that equal volumes of all gases, measured under the same conditions of temperature and pressure, contain equal number of molecules. A mole of a substance contains a fixed no of molecules, applying this law it can be concluded that equal volumes of all gases, measured under the same conditions of temperature and pressure, contain equal number of moles. Then we have

k n or k = nR

where ‘R’ is called molar gas constant and independent of the amount of gas taken

T

PV = nR

PV = nRT

The value of gas constant ‘R’ is same for all gases, hence it is called universal gas constant. To obtain numeric value for R, let us proceed as follows: If 1 mole of an ideal gas is chosen, its volume under standard conditions of temperature and pressure (STP) (i.e., at 0 oC and 760 mm Hg) has been found to be 22.414 lit.

1 atm × 22.414 lit = 1 mole × R × 273.16 oK

R = 0.08205 lit atm/mole deg

The molar gas constant may also be given in energy units by expressing the pressure in dyne/cm2 (1 atm = 1.0133 × 106, volume in cm3 is 22,414 cm3). Then

o

6

16.273

414,22101.0133

T

PVR

= 8.314 × 107 erg/mole deg

or since 1 joule = 107 erg

R = 8.314 Joules/mole deg

The constant can also be expressed in cal/mole deg employing the equivalent, 1 cal = 4.184 joules.

R =

joules/cal 184.4

deg molejoules/ 314.8 = 1.987 cal/ mole deg

Molecular Weight: The approximate molecular weight of a gas can be determined by use of ideal gas law. The number of moles of gas n is replaced by its equivalent g/M in which g is the grams of gas and M is molecular weight.

PV = g/M (RT)

M = PV

gRT

6 | Physical Pharmaceutics – I Kinetic Molecular Theory: The equations just given have been formulated from experimental consideration. This theory was developed to explain the behaviour of gases and to lend additional support to the rancidity of the gas laws is called the kinetic molecular theory. Some of the more important statements of the theory are the following

1. Gases are composed of particles called molecules, the total volume of which is so small as to be negligible in relation to the volume of the space in which the molecules are confined. This condition is approximated in actual gases only at low pressures and high temperatures in which case the molecules of the gas are far apart.

2. The particles of the gas do not attract one another but rather move with complete independence, again this statement applies only at low pressures.

3. The particles exhibit continuous random motion owing to their kinetic energy. The average kinetic energy, E, is directly proportional to the absolute temperature of the gas or

E = 2

3RT

4. The molecules exhibit perfect elasticity, that is there is no net loss of speed after they collide with one another and with the walls of the confining vessel which latter effect accounts for the gas pressure. Although the net velocity and therefore the average kinetic energy, does not change on collision, the speed and energy of the individual molecules may differ widely at any instant.

From these and other postulates, the following fundamental kinetic equation is derived:

21PV nmc

3

where P is the pressure and V the volume occupied by any number n of molecules of

mass m having an average velocity c .

Using the fundamental equation, the root mean square velocity 1

2 2c (usually written )

of the molecules is an ideal gas can be obtained. Solving for 2c in M =

PV

gRT and

taking the square root of both sides of the equation leads to the formula.

= d

3P

M

3RT

nm

PV3

Since the term nm/V is equal to density

States of Matter | 7 In other words, the rate of diffusion of a gas is inversely proportional to the square root of its density. Such a relation confirms the early findings of Graham, who showed that a light gas diffused more rapidly through a porous membrane than diffued a heavier one.

Vander Waals Equation for Real Gases: The fundamental kinetic equation is found to compare with the ideal gas equation, since the kinetic theory is based on the assumption of the ideal state. However, real gases are not composed of infinitely small and perfectly elastic non attracting spheres. Instead, they are composed of molecules of a finite volume that tend to attract one another. These factors affect the volume and pressure term in the ideal equation, so that certain refinements must be incorporated if ideal gas equation is to provide results that check with experiment. A number of such expressions have been suggested, the Vander Waals equation being one of the best known of there for 1 mole of gas, the Vander Waals equation is written as

RT b–V V

aP

2

for n moles of gas in container of volume V is

nRT nb–V V

anP

2

2

The term a/V2 accounts for the internal pressure per mole resulting from intermolecular forces of attraction between the molecules b accounts for the incompressibility of the molecules, that is excluded volume, which is about four times the molecular volume. Polar liquids have high internal pressure and serve as solvents only for substances of similar internal pressure. Non polar molecules have low internal pressure and are not able to overcome the powerful cohesive forces of the polar solvent molecules. Mineral oil is immiscible with water for this reason. When the volume of a gas is large, a/V2 and b becomes insignificant with respect to P and V, respectively. Under these conditions the Vander Waals’ equation for 1 mole of gas reduces to ideal gas equation, PV = RT, and of low pressures, real gases behave in an ideal manner.

1.3 The Liquid State Liquefication of Gases: When a gas is cooled, it loses some of its kinetic energy in the form of heat, and the velocity of the molecules decreases. If pressure is applied to the gas, the molecules are brought within the sphere of the Vander Waals interaction forces and pass into liquid state. Because of these forces, liquids are considerably denser than gases and occupy a definite volume. The transitions from a gas to a liquid and from a liquid to solid depend not only on the temperature, but also on the pressure to which the substance is subjected.

8 | Physical Pharmaceutics – I If the temperature is elevated sufficiently, a value is reached above which it is impossible to liquefy a gas, irrespective of the pressure applied. This temperature above which a liquid can no longer exist is known as the critical temperature. The pressure required to liquefy a gas at its critical temperature is the critical pressure, which is also the highest vapour pressure that the liquid can have. The farther a gas is cooled below its critical temperature the less pressure is required to liquefy it. Based on this principle, all known gases have been liquefied.

The critical temperature of water is 374 oC or 647 oK and its critical pressure is 218 atm, while the corresponding values for helium are 5.2 oK and 2.26 atm. The critical temperature serves as a rough measure of the attractive forces between molecules, for at temperatures above the critical value, the molecules posses sufficient kinetic energy so that no amount of pressure can bring them within the range of attractive forces that cause the particles to stick together. The high critical values for water result because of the strong dipolar forces between the molecules and particularly the hydrogen bonding that exits. Conversely helium molecules are attracted only by the weak London force and consequently this element must be cooled to the extremely low temperature of 5.2 oK before it can be liquefied. Above this critical temperature, helium remains as a gas no matter what the pressure.

Method of Achieving Liquefication: One of the most obvious ways to liquefy a gas is to subject it to intense cold by the use of freezing mixture. Other methods depend on the cooling effect produced in a gas as it expands. Thus, suppose we allow an ideal gas to expand so rapidly that no heat enter the system, such an expansion is termed as adiabatic expansion, may be achieved by carrying out the process in a Dewar, (or) Vacuum flask which effectively insulates the contents of the flask from the external environment. The work that has to be done to bring about expansion therefore must come from the gas itself at the expense of its own heat energy content. As a result, the temperature of the gas falls. If this procedure is repeated a sufficient number of times, the total drop in temperature may be sufficient to cause liquefication of the gas.

A cooling effect is also observed when a highly compressed non ideal gas expands, into a region of low pressure. In this case the drop in temperature results from the energy expanded in over coming the cohesive forces of attraction between the molecules. This cooling effect is known as Joule-Thomson effect and differs from the cooling produced in adiabatic expansion, in which the gas does external work. To bring about liqueficatin by the Joule Thomson effect, it may be necessary to precool the gas before allowing it to expand. Liquid oxygen and liquid air are obtained by methods based on this effect.

Aerosols: Gases can be liquefied under high pressure, provided if it is at below the critical temperature. When the pressure is reduced, the molecules expand and the liquid

States of Matter | 9 reverts to a gas. This reversible change of state is the basic principle involved in the preparation of pharmaceutical aerosols. In such products a drug is dissolved or suspended in a propellant, a material that is liquid under the pressure conditions existing inside the container but forms a gas under normal atmospheric conditions. The container is so designed that, by depressing a volume, some of the drug propellant mixture is expelled owing to the excess pressure inside the container. If the drug is non-volatile it forms a fine spray as it leaves the valve orifice at the sometime, the liquid propellant vapourises off. The propellant used in these products is frequently a mixture of fluorinated hydrocarbons, although other gases, such as nitrogen and CO2 are increasingly used. By varying the proportions of the various propellent it is possible to produce pressures within the container ranging from 1 to 6 atm at room temperature. Alternate fluorocarbon propellants that do not deplete the ozone layer of the atmosphere are perfectly used for investigation.

The containers are filled either by cooling the propellant and drug to a low temperature within the container, which is then sealed with the valve, or by sealing the drug in the container at room temperature and then forcing the required amount of propellant into the container under pressure. In both cases, when the product is at room temperature, part of the propellant is in the gaseous state and exerts the pressure necessary to extrude the drug, while the remainder is in liquid state and provides a solution or suspension vehicle for the drug.

The formulation of pharmaceuticals as aerosols is continuously increasing, since the method frequently offers distinct advantages over some of the more conventional methods of formulation. Thus antiseptic materials can be sprayed on to abraded skin with the minimum of discomfort to the patient. More significant is the increased efficiency often observed and the facility with which medication can be introduced into body cavities and passages.

Vapour Pressure of Liquids: Translational energy of motion (kinetic energy) is not distributed evenly among molecules, some of the molecules have more energy and hence higher velocities than others at any moment when a liquid is placed in an evacuated container at a constant temperature, the molecules with the highest energies break away from the surface of the liquid and pass into the gaseous state, and some of the molecules subsequently return to the liquid state, or condense when the rate of condensation equals the rate of vapourisation at a definite temperature, the vapour becomes saturated and a dynamic equilibrium is established. The pressure of the saturated vapour above the liquid is then known as the equilibrium vapour pressure. If a manometer is fitted to an evacuated vessel containing the liquid it is possible to obtain a record of the vapour pressure in

10 | Physical Pharmaceutics – I millimetre of mercury. The pressure of a gas such as air, above the liquid would decrease the rate of evaporation, but it would not effect the equilibrium pressure of the vapour.

As the temperature of the liquid is evaluated more molecules approach the velocity necessary for escape and pass into gaseous state. As a result the vapour pressure increases with rising temperature as shown in Fig.1.2. At any point on one of the curves represents a condition in which the liquid and the vapour exist together in equilibrium. As observed in Fig. 1.2 if the temperature of any of the liquids is increased while the pressure is held constant or if the pressure is decreased while the temperature is held constant all the liquid will pass into vapour state.

Fig. 1.2 The variation of the vapour pressure of some liquids with temperature

Clausius Calpeyron Equation: The relationship between the vapour pressure and the absolute temperature of liquids expressed by Clausius-Clapeyron equation.

2 12

1 1 2

H T – TPlog

P 2.303 RT T

where P1, P2 are the vapour pressure at absolute temperature T1, T2, H is molar heat of vapourisation i.e., the heat absorbed by 1 mole of liquid when it passes into vapour state.

Boiling Point: If a liquid is placed in an open container and heated until the vapour pressure equals the atmospheric pressure, the vapour is seen to form bubbles that rise rapidly through the liquid and escape into gaseous state. The temperature at which the vapour pressure of the liquid equals to the external or atmospheric pressure is known as boiling point. All the absorbed heat is used to change the liquid to vapour, and the

States of Matter | 11 temperature dose not rise until the liquid is completely vapourised. At high elevation, the atmospheric pressure decreases and boiling point is lowered. At pressure of 700 mmHg, water boils at 97.7 oC at 17.5 mmHg it boils at 20 oC.

The heat that is absorbed when water vaporises at the normal boiling point is 539 cal/gm or about 9720 cal/mole for benzene if its 91.4 cal/gm at normal boiling point of 80.2 oC. These quantities of heat is known as latent heat of vaporisation. The boiling point may be considered as temperature at which thermal agitation can overcome the attractive forces between the molecules of a liquid. Therefore the boiling point of a compound, like the heat of vapourisation and the vapour pressure at a definite temperature, provides a rough indication of the magnitude of attractive forces.

The boiling point of normal hydrocarbons, simple alcohols and carboxylic acids increase with molecular weight, since the attractive Vander Waals forces become greater, with increasing number of atom branching of the chain produces a less compact molecule with reduced intermolecular attraction, and a decrease in the boiling point results. In general, the alcohol boils at a much higher temperature than saturated hydrocarbons of the same molecular weight because of association of alcohol through hydrogen bonding that can remain even in vapour state, the boiling of straight chain primary alcohols and carboxylic acid increase about 18 oC for each additional methylene group. Non polar substances, the molecules of which are held together by London forces, have low boiling point. Polar molecules particularly those such as ethylalcohol and water which are attracted through hydrogen bonding exhibit high boiling point.

1.4 Solids and Crystalline State Crystalline Solids: The structural units of crystalline solids such as ice, sodium chloride and menthol are arranged in fixed geometric pattern or lattices. Crystalline solids, unlike liquids and gases have definite shapes and an orderly arrangement of units. Gases are easily compressed whereas solids, like liquids are practically incompressible. Crystalline solids show definite melting points, passing rather sharply from the solid to the liquid state. The various crystal forms are divided into six distinct crystal systems. They are together with examples of each cubic (NaCl), tetragonal (urea) hexagonal (Iodoform) rhombic iodine, monoclinic (sucrose), and triclinic (boric acid).

The units that constitute the crystal structure can be atom, molecules or ions. The sodium chloride crystal consists of cubic lattice of sodium ions interpenetrated by a lattice of chloride ions, the binding force of crystal being the electrostatic attraction of the oppositely charged ions. In diamond and graphite, the lattice units consists of atom held together by covalent bonds. Solid carbon dioxide, hydrogen chloride, and naphthalene form crystals composed of molecules as the binding units. In organic compounds the molecules are held together by Vander Waals forces and hydrogen bonding, which

12 | Physical Pharmaceutics – I account for the weak binding and for low melting points of these crystals. Aliphatic hydrocarbon crystallize with their chain lying in a parallel arrangement, while fatty acids crystallize in layers of dimers with the chain lying parallel or tilted at an angle with respect to the base plane. Whereas ionic and atomic crystals in general are hard and brittle and have high melting points, molecular crystals are soft and have low melting points.

Metallic crystals are composed of positively charged ions in a field of freely moving electrons, sometimes called the electron gas. Metals are good conductors of electricity because of the free movement of the electrons in the lattice. Metals may be soft or hard or soft and have low or high melting points. The hardness and strength of metals depend in part on the kind of imperfection, or lattice defects in the crystals.

X-Ray Diffraction: X-rays are diffracted by crystals just as visible light is dispersed in a colour spectrum by a rule grating (i.e., a piece of glass with fine parallel lines of equal with drawn on it). This is due to the fact that x-rays have wavelengths of about the same magnitude as the distance between the atoms or molecules of crystals. The x-ray diffractions pattern is photographed on a sensitive plate arranged behind the crystals and by such a method the structure of a crystal may be investigated. Employing a later modification of this principle, involving reflection of the x-ray beam from the atomic planes of the crystals it has become possible to determine the distances of the various planes of crystal lattice. The structure of various compounds can be determined in this way.

Where whole crystals are unavailable or unsuitable for analysis, a powder of the substance may be investigated, comparing the position and intensity of the lines on such a diagram with corresponding lines on the photographs of as known sample allows one to conduct a qualitative and a quantitative chemical analysis.

The electron density and accordingly, the position of the atoms in complex structures such as pencillin may be determined from a mathematical study of the data obtained by x-ray diffraction.

Melting Point and Heat of Fusion: The temperature at which a liquid passes into the solid state is known as the freezing point. It is also the melting point or melting point of a pure crystalline solid is strictly defined as the temperature at which the pure liquid and solid exist in equilibrium. In practice it is taken as the temperature of the equilibrium mixture at an external pressure of 1 atm; this is sometimes known as the normal freezing or melting point.

The heat absorbed when a gram of a solid melts or the heat liberated when it freezes is known as the latent heat of fusion and for water at 0 oC it is about 80 cal/g (1436 cal/mole). The heat added during the melting process does not bring about a change in temperature until all of the solid has disappeared, since this heat is converted into the potential energy of the molecules that have escaped from the solid into the liquid state.

States of Matter | 13 Changes of the freezing or melting point with pressure may be obtained by using one form of the Clapeyron equation. It is written

f

s

ΔH

v–vT

P

T l

where vl and vs are the molar volumes of the liquid and solid respectively. Molar volume (vol. in cm3 per mole) is computed by dividing by gram molecular weight by the density of the compound. Hf is molar heat of fusion, that is the amount of heat absorbed when 1 mole of the solid changes into 1 mole of liquid, and T is the change of melting point brought about by a pressure change of P.

Water is unusual in that it has a lager molar volume in the solid state than in the liquid state (vs > vl) at the melting point. Therefore, T/P is negative, signifying that the melting point is lowered by an increase in pressure. This phenomenon can be rationalised in terms of Lechatelier’s principle, which states that a system at equilibrium readjusts so as to reduce the effect of an external stress. Accordingly if a pressure is applied to ice at 0 oC, it will be transformed into liquid water, that is into the state of lower volume, and the freezing point will be lowered.

Hence an increase of pressure of 1 atm lowers the freezing point of water by about 0.0075o, or an increase in pressure of about 133 atm would be required to lower the freezing point of water by1o. Pressure has only a slight effect on the equilibrium temperature of condensed system the large volume or low density of ice accounts for the fact the ice floats on liquid water. The lowering of melting point with increasing pressure is taken advantage of in ice skating. The pressure of the skate lowers the melting point and thus causes the ice to melt below the skate. This thin layer of liquid provides lubricating action allows the skate to state also contributes greatly to the melting and lubricating action.

Melting Point and Intermolecular Forces: The heat of fusion may be considered as the heat required to increase the interatomic or intermolecular distances in crystals, thus allowing melting to occur. A crystal that is bound together by weak forces has a low heat of fusion and a low melting point and crystals which are bound together by strong forces will have a high heat of fusion and high melting points.

Paraffins crystallize as thin leaflets composed of zig-zag chains packed in a parallel arrangement. The melting points of normal saturated hydrocarbons increase with molecular weight because the Vander Waals force between the molecules of the crystal and become greater with an increasing number of carbon atoms. The melting points of the alkanes with an even number of carbon atoms are higher than those of the hydrocarbons with an odd number of carbon atoms. This phenomenon presumably is due to the fact that alkanes with an odd number of carbon atoms are packed in the crystal less efficiently.

The melting points of normal carboxylic acids also show this alteration. This can be explained as follows: fatty acids crystallize in molecular chains. The even carbon acids

14 | Physical Pharmaceutics – I are arranged in the crystal as seen in the more symmetric structure I, whereas the odd numbered acids are arranged according to structure II. The carboxyl groups are joined together at two points in the even carbon compound; hence the crystal lattice is more stable and the melting point is higher.

The melting points and solubilities of the xanthines of pharmaceutical interest determined by Guttman and Higuchi further exemplify the relationship between melting point and molecular structure. Solubilities like mleting points, are strongly influenced by intermolecular forces. The methylation of theophylline to form caffine and lengthening of the side chain from methyl (caffine) to propyl in the 7th position results in decreases of the melting points and in increase in solubilities. These effects presumably are due to progressive weakening of intermolecular forces.

Polymorphism: Some substances has got the property of existing in different forms. This property is known as polymorphism and the forms are referred to as polymorphs. And if the substance is an element then the property is known as allotropy.

Among the polymorphs some are stable and some are less stable. The less stable forms are known as metastable form. And sometimes the less stable forms are converted in to a stable form and this property is known as monotrophy. Sometimes the polymorphs interchanges between themselves according to the environmental conditions like temperature etc. This property is known as enantiotropy. The temperature at which inter conversion of the poymorphs takes place is known as transition temperature, and the process is known as transition.

Different theories has been proposed to explain the stability of polymorphs. These are based up on different criteria.

1. Based on Free Energy: According to this the polymorph with less free energy is referred to as the most stable one.

2. Heat of Transition Rule: If the endothermic transition takes place for the given polymorphs then both the polymorphs bear the enantiotrophic relationship at a lower temperature. If these takes place an exothermic transition then the given polymorphs may have a monotrophic relationship or at the temperature higher than the exotherm then they bear an exothermic relationship.

3. Heat of fusion rule.

4. Density Rule: The most dense form will be the most stable one at the absolute zero. But this is applied only for the molecular solids where the intra-molecular hydrogen bonding is not significant.

The polymorphs are formed because of the differences in the arrangement of the unit cells. Because of the differences in arrangement, the different properties like heat capacity, conductivity, volume, density, viscosity, surface tension, diffusivity crystal hardness, crystal shape, refractive index, melting or sublimation properties, latent heat of fusion, stability, solubility etc arises in the polymorphs.

States of Matter | 15 As the polymorphs of the same substance has got the different properties it is necessary to study them. The polymorphs have different melting points, x-ray diffraction patterns and solubilities but they are chemically identical.

Generally the property of polymorphism is exhibited by longchain fatty acids because of the attachment difference between the carboxyl groups of adjacent molecules.

Triglyceride tristearin has three forms (three polymorphs)

They are metastable () → low melting point

Betaprine ( ' ) form

Stable beta () form → high melting point

The conversion of metastable to stable form takes place but the vice-versa is not possible.

Theobromo oil or cocoabutter is used as a suppositoty base. And it has got four polymorphs. It consists of a single glycerida which has got the narrow temperature range (34 – 36 oC). The four polymorphs are:

Unstable gamma → m.p. – 18 oC

Alpha form → m.p. – 22 oC metastable forms

Beta prime form → m.p. – 28 oC

Stable Beta form → m.p → 34.5 oC + stable form

In the preparation of suppository we have to melt the base and it should be poured into the moulds, for that purpose we have to heat it. If we heat the theobromo oil to 35 oC where it is completely liquefied then the nuclei of the stable form gets destroyed. And it does not crystallize until it is super cooled to 15 oC. So formed crystals are the metastable forms which melt at 23o to 24 oC. But such type of bases are not useful for the preparation of suppositories. So we have to heat the theobromo oil to 33 oC where it will be in a state of liquid which is quite enough to be poured into the moulds. At this state the nuclei of the stable Beta form will also be retained. And after cooling the suppositories are formed which will be having a melting point of 34.5 oC.

Polymorphs will be having thus different solubilities. If the solubility of drug is less than the rate of dissolution and the bioavailability of drug is also less. For example, chloromphenicol palmiate is very much influenced by this polymorphism.

Sulfameter → antibacterial agent → form II is more active orally than form III.

Suspension Technology: Cortisone acetate occurs in five different forms. Of these 4 forms are unstable. These will change into a stable polymorph in the presence of water or heating or grinding. Due to this caking of the crystals will be observed due to which the suspension stability will be effected. Because of this reason only before formulating the (emulsion) suspension, cortisone acetate should be in a stable form.

16 | Physical Pharmaceutics – I Spiperone (Antipsychotic agent) has got two polymorphs and the arrangement of the crystal or crystal structure of both these polymorphs is different. Polymorph II is made up of dimers. The polymorph I consists of nondimerized molecules.

The difference in the intermolecular Vander Waals forces and hydrogen bonding were found to produce different crystal structures in the antisychotrophic drugs like haloperiodol.

Hydrogen bonding difference led to polymorphism in sulphonamides.

Tamonifen citrate – Antiestrogenic and antineoplastic drug

(used in treatment of breast cancer)

It consists of form A and form B

Form B: it consists of hydrogen bonding which is formed between the carboxyl group of citric acid and the nitrogen of next tamonifen.

Form A: metastable polymorph. But its molecular structure is less organised. Ethanolic suspension of polymorph A rearranges into polymorph B.

Carbamazepines: used in the treatment of epilepsy and trigeminal neuralgia (severe pain in the face, lips and tongue).

polymorph is crystallised from solvents of high dielectric constant (such as aliphatic alcohols) on the other hand polymorph is crystallised from solvents of low dielectric constant (e.g., CCl4 and cyclohexane).

Estrogens are essential hormones for the development of female sex characteristics. When the potent synthetic estrogen, ethyxylestradiol is crystallised from the solvents acetonitrile, methanol, and chloroform saturated with water, four different crystalline solvents formed. Ethxylestradiol has been reported to exist in several polymorphic forms. However, Ishida et. al., have now shown from thermal analysis infrared spectroscopy and x-ray studies that these forms are crystals containing solvent molecules and thus should be classified as solvates rather than as polymorphs. Solvates are sometimes called pseudo polymorphs.

Amorphous Solids: Amorphous solids may be considered as super cooled liquids in which the molecules are arranged in a random manner, somewhat as in the liquid state. Substances such as glass, pitch, and many synthetic plastics are amorphous solids. They differ from crystalline solids in that they tend to flow when subjected to sufficient pressure over a period of time, and they do not have definite melting points.

Amorphous substances as well as cubic crystals, are usually isotropic, that is they exhibit similar properties in all direction. Crystals other than the cubic are anisotrophic, showing different characteristics in various directions along the crystal.

States of Matter | 17 It is not always possible to determine by casual observation whether a substance is crystalline or amorphous. Bees wax and paraffin, although they appear to be amorphous, assume crystalline arrangement when heated and then allowed to cool slowly. Petrolatum as already mentioned, contain both crystalline and amorphous constituents. Some amorphous materials such a glass, may crystallize after long standing.

Whether drug is amorphous or crystalline, it has been shown to affect its therapeutic activity. Thus the crystalline form of the antibiotic novobiocin acid is poorly absorbed and has no activity, whereas the amorphous form is readily absorbed and therapeutically active.

Liquid Crystalline State: The liquid crystal is an apparent contradiction, but it is useful in a descriptive sense since materials in this state are in many ways intermediate between the liquid and solid states.

Structure of Liquid Crystals: Generally molecules in the liquid state are mobile in three directions and can also rotate about three axes perpendicular to one another. On the other hand, in the solid state the molecules are immobile and rotations are not possible.

It is not unreasonable to suppose, therefore that intermediate states of mobility and rotation should exists as in fact they do. It is these intermediate states that constitute the liquid crystalline phase or mesophase as the liquid crystalline phase is called.

The two main types of liquid crystals are termed smectic (soap or grease like) and nematic (thread-like). In the smectic state, molecules are mobile in two direction and can rotate about one axis. In the nematic state, the molecules again rotate only about one axis but mobile in three dimension. A third type (cholesteric crystals) exists but may be considered as a special case of the nematic type.

The smectic mesophase is probably of most pharmaceutical significance since it is this phase that usually forms in ternary (or more complex) mixtures containing a surfactant, water is a weakly amphiphilic or nonpolar-additive.

In general, molecules that form mesophases are organic, are elongated and rectilinear in shape are rigid and posses strong dipoles and easily polarizable groups. The liquid crystalline state any result either from the heating of solids (thermotrophic liquid crystals) or from the action of certain solvents on solids (lyotrophic liquid crystals).

Properties and significance of liquid crystals: Because of their intermediate nature, liquid crystals have some of the properties of liquids and some of solids. For e.g., liquid crystals are mobile and thus can be considered to have the flow properties of liquids. At the same time they possess; the property of being birefringence, the light passing through a material is divided into two components with different velocities and hence different refractive indices.

Some liquid crystals show consistent colour changes with temperature, and this characteristic has resulted in their being used to detect areas of elevated temperature under the skin that may be due to a disease process. Nematic liquid crystals are sensitive

18 | Physical Pharmaceutics – I to electric fields a property used to advantage in developing display systems. The smectic mesophase has application in the solubilization of water-insoluble materials. It also appears that liquid crystalline phases of this type are frequently present in emulsion and may be responsible for enhanced physical stability owing to their highly viscous nature.

The liquid crystalline state is widespread in nature, with lipoidal form found in nerves, brain tissue, and blood vessels. Atherosclerosis may be related to the laying down of liquid in the liquid crystalline state on the walls of the blood vessels. The three components of bile (cholesterol, a bile acid salt and water) in correct proportions, can form a smectic mesophase, and this may be involved in the formation of gallstones. Bogardus applied the principle of liquid crystal formation to the solubilization and dissolution of cholesterol the major constituent of gallstones. Cholesterol is converted to a liquid crystalline phase in the presence of sodium oleate and water, and the cholesterol, rapidly dissolves from the surface of gallstones.

Non aqueous liquid crystals may be formed from triethanol amine (TEA) and oleic acid with a series of poly ethylene glycols or various organic acids such as isopropyl myristate, squalene, squalene and naphthenic oil as the solvents to replace the water of aqueous mesomorphs. Triangular plots or tetiary phase diagram were used to show that the regions of the liquid crystalline phase when either polar (polyethylene glycols) or nonpolar (squalene) etc compounds were present as a solvent.

Ibrahim studied the release of salicyclic acid as a model drug from hypotrophic liquid crystalline systems a cross lipoidal barriers and into an aqueous buffered solution.

Finally the liquid crystals have structure that are believed to be similar to those in cell membranes. As such liquid crystals may function as useful biophysical models for the structure and functionality of cell membrane.

1.5 Phase Equilibria and the Phase Rule

The condition relating to physical equilibria between various states of matter are conveniently expressed by phase rule. In order to understand this rule, it is first necessary to explain what is meant by the term ‘phase’, number of components, and ‘degrees of freedom’.

Phase (P): A phase is defined as any homogenous and physically distinct part of a system that is separated from other parts of the system by definite boundaries.

e.g., A mixture of gases always constitute one phase because the mixture is homogenous and there are no bounding surfaces between the different gases in the mixture.

States of Matter | 19

No. of Components (C): The no. of components of a system is the smallest no. of independent chemical constituents necessary to express the conc of all phases present in the system.

e.g., In the case of three phase system ice, water and water vapour, the no. of components is one. Since each phase can be expressed in terms of H2O. A mixture of salt and water is a two component system since both chemical species are independent.

Degrees of Freedom (7): The no. of degrees of freedom is the no. of variable conditions such as temperature, pressure and concentration that it is necessary to state. In order that the condition of the system at equilibrium may be completely define refractive index, density, viscosity etc.

J.Willard tibbs is the person who has formulated the phase rule relating the effect of the least no. of independent variables upon various phases (solid, liquid, gas) that can exist in an equilibrium system containing a given no. of components.

The phase rule is expressed as

F = C – P + 2 F-degrees of freedom

C-No. of components

P-phase

Generally the phase rule is used to define the no. of degrees of freedom that exists for a given system.

E.g., for instance if we consider a gas at a particular temperature then the temperature itself is not sufficient to completely define the system either we must have pressure or other parameters of the system which varies independently with volume regarding to temperature. Then it is clear that this type of system requires two degrees of freedom in order to completely define the system

F = 1 – 1 + 2 = 2

This is also (proved) confirmed by the phase rule.

Next if we consider a system with water and its vapour then this system can be completely defined by using one variable also became let it be temperature because. The pressure at which the both the phase coexists is also defined

F = 1 – 2 + 2 = 1

Again this is confirmed by the phase rule.

20 | Physical Pharmaceutics – I 1.5.1 Systems Containing One Component

Fig. 1.3 Phase diagram for water at moderate temperature and pressure.

The phase diagram for ice-water-water vapour system may be used to illustrate the interpenetration of these diagrams for one-component system. This particular diagram is also of importance in the understanding the process of freeze drying.

Here in the Fig. 1.3 the areas each correspond to a single phase. The no. of degrees of freedom is given by

F = 1 – 1 + 2 = 2

This means that temperature and pressure can be varied independently in these areas. For e.g., by varying the temperature and pressure, a mass of water under condition corresponding to point w1, may be converted to a mass at higher temperature and pressure at point w2 i.e., this independent variation of temperature and pressure has not altered the no. of phases in the system. However if the conditions are such that the system corresponds to a point that lies on one of the lines AO, BO or CO then two phases now exist in equilibrium with each other, since these lines form the boundaries between different phases. The no. of degrees of freedom is reduced because from eq.

F = C – P + 2 F = 1 – 2 + 2 = 1

This means that a single variable exists when equilibrium is established between two phases and if the pressure is altered, the temperature will assume a particular value or conversely if the temperature is altered, the pressure will have a definite value.

States of Matter | 21

Triple Points: The boundary line meet at ‘O’ which is the only point in the diagram

where three phases may coexist in equilibrium and its is therefore termed a triple point.

The applications of the phase rule equations to the system at ‘O’ shows that

f = 1 – 3 + 2 = 0

The system is therefore invariant, i.e., any change in pressure or temperature will

result in an alteration of the no. of phases that are present.

The triple point for water occurs at a temperature of 273.1598 K and a pressure of

610 N/m2. Thus the triple point temperature is 0.0098 oC above the usual freezing point of

water at 1.01325 × 105 N/m2.

Condensed System: Systems in which the vapour phase is ignored and only solid and/or

liquid phases are considered are termed as condensed systems.

Zeotrophic Mixture: Systems where the total vapour pressure is always intermediate

between those of the pure components i.e., there is neither as maximum nor minimum in

the vapour pressure composition.

e.g., CCl4, Cyclohexane, H2O and Methanol

Fig. 1.4

22 | Physical Pharmaceutics – I For the purpose of explaining the effects of distillation it is more convenient to use a phase diagram that shows the variation in boiling point with composition of the liquid and vapour phase at constant pressure. It should be observed that the upper and lower curves represent the vapour composition and liquid composition respectively and that the areas corresponding to liquid and vapour phases are transported when compared with the vapour pressure diagrams.

Kon Walff’s rule (the vapour pressure in equilibrium with a particular liquid composition is richer in the more volatile component i.e., the component with a higher vapour pressure) can still be seen to apply in the boiling point diagram, since a liquid with a composition corresponding to l1, will boil at temperature T1 and be in equilibrium with vapour of composition l2. This vapour is therefore richer in component A1 which has the lower boiling point (TA) and is therefore the more volatile component of the liquid mixture.

If the vapour of composition l2 is removed and condensed it will give a liquid of composition l2. If this liquid is subsequently heated it will boil at temperature T2 to provide a vapour of composition l3 that is even richer in component A; i.e., the composition of the distillate will approach closer to pure A as more stages of heating and condensation are involved. Conversely as vapour that is richer in A is removed from the distillation flask, the composition of the liquid remaining in the flask gradually approaches pure B. Thus, the components of a zeotrophic mixture may be separated completely by the process of fractional distillation which involves the occurrence of many individual stages of vapourisation and condensation in a distillation column.

Fig. 1.5 Vapour pressure diagram showing liquid and vapour composition curves (zeotrophic mixture)

States of Matter | 23

Fig. 1.6 Boiling point composition diagram of a zeotrophic system

If the phase rule is applied to the two component system in the distillation flask where two phase (i.e., liquid and vapour) are present it can be shown that two degrees of freedom exist

f = 2 – 2 + 2 = 2

Since the pressure is kept constant, the temperature will therefore change as the composition varies in order to maintain the same no. of phase. i.e., the boiling point of the liquid remaining in the flask increases as its composition approaches pure B.

1.5.2 Partially Miscible Liquids

Systems Showing an Increase in Miscibility with Rise in Temperature: A positive deviation from Raoults law arises from a difference in the cohesive forces that exist between the molecules of each component in a liquid mixture. This difference become masked as the temperature decreases, and the positive deviation may then result in a decrease in miscibility sufficient to cause the separation of the mixture into two phases. Each phase consists of a saturated solution of one component in the other liquid. Such mutually saturated solutions are known as conjugated solutions.

The equilibria that occur in mixtures of partially miscible liquid may be followed either by shaking the two liquids together at constant temperature and analysing the samples from each phase after equibrium has been attained, or by observing the temperature at which known proportion of the two liquids contained in the sealed glass ampules become miscible as shown by the disappearance of turbidity.

24 | Physical Pharmaceutics – I We know from experience that ethyl alcohol and water are miscible in all proportions, where as water and mercury are for all practical purposes completely immiscible regardless of the relative amounts of each present. Between these two extremes lies a whole range of systems that exhibit partial miscibility (or immiscibility). Such a system is phenol and water and a portion of condensed phase diagram is plotted. The curve gbhci shows the limits of temperature and concentration within which two liquid phases exist in equilibrium. The region outside this curve contains systems having only one liquid phase

Fig. 1.7 Temperature–composition diagram for the system consisting of water and phenol.

starting at the point a, equivalent to a system containing 100% water (i.e., pure water) at 50 oC, the addition of known increments of phenol to a fixed weight of water, the whole being maintained at 50 oC, will result in the formation of a single liquid phase until the point b is reached at which a minute amount of a second phase appears.

The concentration of phenol and water at which this occurs is 11% by weight of phenol in water. Analysis of the second phase, which separates out on the bottom, show it to contain 63% by weight of phenol in water. This phenol rich phase is denoted by the point C on the phase diagram. As we prepare mixtures containing increasing quantities of phenol, that is as we proceed across the diagram from point b to point c, we form systems in which the amount of the phenol rich phase (B) continually increases as denoted by the test tube. At the same time, the amount of the water rich phase (A) decreases. Once the total concentration of phenol exceeds 63% at 50o, a single phenol-rich liquid phase is formed.

States of Matter | 25

The maximum temperature at which the two phase region exists is termed the critical solution, or upper consolute temperature. In the case of the phenol and water above this temperature are completely miscible and yield one-phase liquid systems.

The line bc drawn across the region containing two phases is termed a tie-line; it is always parallel to the base line in two compound systems. An important feature of phase diagrams is that all systems prepared on a tie line, at equilibrium, will separate into phase of constant composition. These phases are termed conjugate phases. For example, any system represented by a point on the line bc, at 50 oC, seperates to give a pair of conjugate phase whose composition is b and c. The relative amounts of the two layers or phases vary. Thus if we prepare a system containing 24% by weight of phenol and 76% by weight of water (point d) at equilibrium we have two liquid phases present in the tube. The upper one A, has a composition of 11% phenol in water (point b or the diagram) while the lower layer, B, contains 63% phenols (point C on the diagram). Phase B will lie below phase A since it is rich in phenol and phenol has a higher density than water. In term of the relative weights of the two phases, there will be more of the water-rich phase A then the phenol-rich phase B at point f.

Thus,

bdLength

dcLength

B phase ofWeight

A phase of Weight

The right hand term might appear at first glance to be the reciprocal of the proportion

one should write. The weight of phase A is greater than phase B, however became point d

is closer to point b than it is to point c. The lengths dc and bd can be measured with a

rules in centimetres or inches from the phase diagram, but it is frequently more

convenient to use the units of percent weight of phenol on the abscissa. For e.g., since

point b = 11%, point c = 63% and point d = 24%, the ratio dc/bd = (63 – 24)/ (24 – 11) =

39/13 = 3/1. In other words, for every 10 gm of a liquid system in equilibrium represented

by point d, one finds 7.5 gm of phase A and 2.5 gm of phase B. If, on the other hand, we

prepare a system containing 50% by weight of phenol (point f), the ratio phase A to phase

B = fc/bf = (63 – 50)/(50 – 11) = 13/39 = 1/3. Accordingly for every 10 gm of system f

prepared, we obtain an equilibrium mixture of 2.5 gm of phase A and 7.5 gm of phase B.

It should be apparent that a system containing 37% by weight of phenol will under

equilibrium conditions at 50 oC, give equal weights of phase A and phase B.

26 | Physical Pharmaceutics – I

Working on a tie line in a phase diagram enables us to calculate the composition of

each phase in addition to the weight of the phases. Thus, it becomes a simple matter to

calculate the distribution of phenol (or water) through out the system as a whole. As an

example let us suppose that we mixed 24 gm of phenol with 76 gm of water, warmed the

mixture to 50 oC, and allowed it to reach equilibrium at this temperature. On separation of

the two phases, we would find 75 gm of phase A (containing 11% by weight of phenol)

And 25gm of phase B (containing 63% by weight if phenol). Phase A therefore contains

a total of (11 × 75)/100 = 8.25 gm of phenol, while phase B contains a total of (63 ×

25)/100 = 15.75 gm of phenol. This gives a sum total of 24 gm of phenol in the whole

system. This equals the amount of phenol originally added and therefore confirm our

assumptions and calculations. It is left to the reader to confirm that phase A contains

66.75 gm of water and phase B 9.25 gm of water.

Phenol and water system has got many pharmaceopeal applications. Some of the other

combinations are water-aniline, carbon-disulphide-methyl alcohol, isopentane-phenol

methyl alcohol-cyclohexane and isobutyl alcohol-water.

Some of the mixtures consists of lower consolute temperatures below which both the

liquids are miscible in all proportion e.g., for that type of system is triethylamine-water

system.

Fig. 1.8 Phase diagram for the system triethylamine – water showing lower consolute

temperature.

States of Matter | 27

Some of the mixtures shows both lowers and upper consolute temperature.

e.g., nicotine-water system

Fig. 1.9 Nicotine-water system showing upper and lower consolute temperature.

Two component systems containing solids and liquids phases. The behaviours of two

component solid-liquid systems can e classified into three types.

1. Systems that show the formation of a Eutectic mixture.

2. Systems that show the formation of a compound with a congruent melting point

(i.e., the compound which consists of one component solvated by the other, yields

a liquid with the same composition as the compound on mleting).

3. Systems that show the formation of a compound with an incongruent melting point

i.e., the compound undergoes fusion on heating to a certain temperature and

produces a liquid and a new solid phase, the composition of which is different from

that of the original compound.

System of the first type, which involve the formation of a eutectic mixture, have found

certain applications of pharmaceutical interest. The other types are of less importance.

28 | Physical Pharmaceutics – I 1.5.3 Formation of Eutectic Mixtures

The ice-kcl system shows the behaviour of a entectic mixture.

Fig. 1.10 Temperature composition diagram for the KCl-water system.

Here A and B represent the meting points of ice and kcl respectively. If KCl is added to water, the freezing point of the latter is reduced as indicated by AC, which therefore represents the effect of composition on the temperature at which ice separates from the system. Similarly if water is added to KCl the melting point of the latter is lowered, BC therefore represents the effect of composition on the temperature at which solid KCl separates from the system.

At C, both solid components can exist in equilibrium, with a liquid of definite composition. Application of the ‘reduced phase rule’ shows that the system is invariant at this point since there are no degrees of freedom 'f = 2 + 1 – 3 = 0

This means that the mixture will freeze completely at a constant temperature D, which is lower than the freezing points of either pure component.

Further understanding of the phase diagram may be obtained by considering the effect of cooling a solution of KCl in water represented by point w in the diagram. If the solution is cooled to point x on the freezing curve AC, then some ice will separate out. Further cooling to y will produce more ice and the remaining solution will become more concentrated since it will contain all the original KCl. The composition of the remaining solution will correspond to point z. As the temperature falls, the composition of the remaining liquid moves along AC. A limit is reached when the remaining solution is

States of Matter | 29 saturated with kcl and on cooling this solution ice and KCl will seperate out in the same ratio in which they exist in the saturated solution has solidified. The mixture, which separates at this temperature termed as eutectic (or a cryohydrate, if one of the components is water) and its composition is given by E. Although the eutectic has a definite melting point, the following evidence suggests that it is an intimate mechanical mixture and not a compound.

(a) The components can be separated mechanically

(b) The addition of each component raises the melting point of the eutectic. The melting point of a compound would be lowered on admixture with another substance.

(c) A heterogeneous structure can be seen under a microscope

(d) X-ray analysis reveals the existence of two phases.

The areas in the phase diagram each correspond to the existence of various phases or mixtures of phases.

The phase-diagram for the water-KCl system may be used to explain the principle of freezing mixture prepared from ice and salt. If salt is added to ice and a little water, some of the salt will dissolve in the water to produce a system composed of ice, salt and solution. Such a system II in stable equilibrium at the eutectic point only. The system will therefore tend to move towards this point and ice will melt and salt will continue to dissolve in the resultant water. Both of these processes are accompanied by absorption of heat and the temperature therefore falls until one of the solid components has been used up completely. If the initial proportion of ice and salt are chosen satisfactory the eutectic temperature will be reached.

It has been suggested that eutectic mixtures may be useful as a means of increasing the rates of solution of slowly soluble drugs in a aqueous body fluids. It was thought that the rapid solution of the second component (e.g., urea in eutectic fine crystalline form that would be more rapidly in a very fine crystalline form that would be more rapidly soluble than the usual forms of the drug. However subsequent studies have suggested that this increased dissolution rates of the drugs in the presence of urea is likely to be caused by the formation of solid solutions of these drugs with urea and not by eutectic formation.

1.5.4 Phase Equilibria in Three Component Systems

In systems containing three components but only one phase f = 3 – 1 + 2 = 4 for a noncondensed system. The four degrees of freedom are temperature, pressure and the concentration of two of the three components. Only two concentration terms are required became the sum of these substracted from the total will give the concentration of the third component. If we regard the system as condensed and hold the temperature constant then

30 | Physical Pharmaceutics – I F = 2 and we can again use a plane diagram to illustrate the phase equilibria, because we are dealing with a three component system. It is more convenient to use triangular coordinate graphs, although it is possible to use rectangular co-ordinates.

The various phase equilibria that exist in three-component systems containing liquid and/or solid phases are frequently complex. Certain typical three-component systems are discussed here, however, because they are of pharmaceutical interest, for example, several areas of pharmaceutical processing such as crystallization, salt form selection, and chromatographic analyses rely on the use of terenary systems for optimization.

Rules Relating to Triangular Diagrams

Before discussing phase equilibria interenary systems, it is essential that the reader become familiar with certain rules that relate to the use of triangular co-ordinates. It should have been apparent in discussing two component systems that all concentrations were expressed on a weight-weight basis this is because, although it is an easy and direct method of preparing dispersion, such an approach also follows the concentration to be expressed in terms of the mole fraction or the molality. The concentration in ternary systems are accordingly expressed on a weight basis.

1. Each of the three corners of apexes of the triangle represent 100% by weight of one component (A, B or C). As a result that same apex will represent 0% of the other two components.

2. The three lines joining the corner points represent two component mixtures of the three possible combinations of A, B, and C. Thus the lines AB, BC and CA are used for two component mixtures of A and B, B and C, and C and A respectively. By dividing each line into 100 equals units, we can directly relate the location of a point along the line to the percent concentration of one component in a two component system. For e.g., point y midway between A and B on the line AB, represents a system containing 50% of B (and hence 50% of A also) point z, three fourths of the way along BC, signifies a system containing 75% of c in B.

In goining along a line bounding the triangle so as to represent the concentration in a two components system, it does not maters whether we proceed in a clockwise or a counter clock rise direction around the triangle provided we are consistent. The move usual convention is clockwise and have been adopted here. Hence as we move along AB in the direction of B, we are signifying systems of A and B containing increasing concentrations of B and correspondingly smaller amounts of A. moving along BC toward C will represent systems of B and C containing more and more of C; the closer we approache A on the line CA the greater will be the concentration of A in systems of A and C.

States of Matter | 31

Fig. 1.11 Triangular diagram for three component system.

3. The area within the triangle represents all the possible combinations of A, B, and C to give three component systems. The location of x particular three component system within the triangle for e.g., point can be undertaken as follows:

The line AC opposite apex B represents systems containing A and C component B is absent that is B = 0. The horizontal lines running across the triangle parallel to AC denote increasing percentages of B from B = 0 (on line AC) to B = 100 (at point B), the line parallel to AC that cuts point x is equivalent to 15% B, consequently the systems contains 15% of B and 85% of A and C together. Applying similar arguments to the other two components in the system, we can say that along the line AB, C = 0. As we proceed from the line AB towards across the diagrams C the concentration of C increase until at the apex C = 100%. The point x lies on the line parallel to AB that is equivalent to 30% of C. It follows therefore that the concentration of A is 100 – (B + C) = 100 – (15 + 30) = 55%. This is readily confirmed by proceeding across the diagram from the line BC towards apex A; point x lies on the line equivalent to 55% of A.

4. If a line is drawn through any apex to a point on the opposite side, then all the systems represented by points on. Such a line have a constant ratio of two components in this case A and B. Further more, the continual addition of C to a mixture of A and B will produce systems that lie progressively closer to apex C (100% of component C).

32 | Physical Pharmaceutics – I 5. Any line drawn parallel to one side of the triangle for example line HI represents

ternary system in which the proportion (or percent by weight) of one component is constant. In this instance all systems prepared along HI will contain 20% of C and varying concentration of A and B.

1.5.5 Terenary System with One Pair of Partially Miscible Liquids

Water and benzene are miscible only to a slight extent and so a mixture of the two usually produces a two phase system. The heavier of the two phases consists of water saturated with benzene while the lighter phase is benzene saturated with H2O. On the other hand, alcohol is completely miscible with both benzene and water. It is to be expected therefore that the addition of sufficient alcohol to a two phase system of C4H6 and H2O would produce a single liquid phase in which all three components are miscible. It might be helpful to consider the alcohol as acting in a manner comparable to that of temperature in the binary phenol-water system considered earlier. Raising the temperature of the phenol-water system led to complete miscibiling of the two conjugate phases and the formation of one liquid phase. The addition of alcohol to the benzene-water system achieves the same end but by different means, namely a solvent effect in place of a temperature effect. There is a strong similarity between the use of heat to break cohesive forces between molecules and the use of solvent to achieve the same result. The effect of alcohol will better understood when we introduce dielectric constant of solutions and solvent in later chapters. In this case alcohol serves as an intermediate polar solvent that shifts the electronic equilibrium of a diametrically opposed highly polar water and nonpolar benzene solutions to provide salvation.

Fig. 1.12 System of three liquids, one pair of which is partially miscible.

Let us suppose that A, and B and C represent water, alcohol and benzene respectively. The line AC therefore depicts bindary mixtures of A and C and the points a and c are the limits of solubility of C in A and of A in C respectively at the particular temperature being used. The curve afdeic frequency termed a binodal or binodal, marks curve or binodal, marks the extent of the phase region. The remainder of the triangle contains one liquid phase. The tie lines within the binodal are not necessarily parallel to one another or

States of Matter | 33 to the base line, AC as was the case in the two phase region of binary system. In fact the directions of the tie lines are related to the shape of the binodal which in turn depends on the relative solubility of the third component (in this case, alcohol) in the other two components. Only when the added component acts equally on the other two components to bring them into solution will the bionodal be perfectly symmetric and the tie line run parallel to the base line.

The properties of tie lines discussed earlier still apply and system g and h prepared along the tie line fi both give rise to two phases having the composition denoted by the points f and i. The relative amounts by weight of the two conjugate phase will depend on the position of the original system along the tie line. For e.g., system g after reaching equilibrium will separate into two phases f and i; the ratio of phase f to phases on a weight basis is given by the ratio gi is fg. Mixture h, halfway along the tie line, will contain equal weights of the two phases at equilibrium.

The phase equilibria depicted here show that the addition of component B to a 50:50 mixture of components A and C will produce a phase change from a two liquid system to a one-liquid system at point d, with a 25:75 mixture of A and C shown as point j; the addition of B leads to a phase change at point e. Naturally all mixtures lying along dB and eB will be one phase systems.

As we saw earlier f = 2 in a single-phase region and so we must defined two concentration to fix the particular system. Along the binodal curve afdeic F = 1 and we need to know only one concentration term because this will allows the composition of one phase to be fixed on the binodal curve from the tie line, we can obtain the composition of the conjugate phase.

1.6 Questions 1. Write a short notes on Hydrogen Bonding.

2. What is polymorphism. Give its application in Pharmacy.

3. With the help of a neat labelled diagram explain the phase diagram of phenol water system. How is the tie line useful in calculating the composition of the conjugate layers.

4. Describe the principle involved in aerosols as gaseous dosage forms.

5. List out the different binding forces between the molecules.

6. Write about heat of vaporisation and Heat of a reaction.

7. Mention and explain the important postulates of kinetic molecular theory.